共查询到20条相似文献,搜索用时 593 毫秒
1.
《Waves in Random and Complex Media》2013,23(2):234-248
A hybrid finite element–boundary integral–characteristic basis function method (FE-BI-CBFM) is proposed for an efficient simulation of electromagnetic scattering by random discrete particles. Specifically, the finite element method (FEM) is used to obtain the solution of the vector wave equation inside each particle and the boundary integral equation (BIE) using Green's functions is applied on the surfaces of all the particles as a global boundary condition. The coupling system of equations is solved by employing the characteristic basis function method (CBFM) based on the use of macro-basis functions constructed according to the Foldy–Lax multiple scattering equations. Due to the flexibility of FEM, the proposed hybrid technique can easily deal with the problems of multiple scattering by randomly distributed inhomogeneous particles that are often beyond the scope of traditional numerical methods. Some numerical examples are presented to demonstrate the validity and capability of the proposed method. 相似文献
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J. Luczka 《Journal of statistical physics》1986,45(1-2):309-317
A linear first-order equation with a quadratic colored noise is considered. An exact one-dimensional probability distribution of the process is obtained from the characteristic function. The characteristic function is calculated by means of special functionals of the noise. An auxiliary set of three ordinary differential equations (which contains a Riccati equation) is solved for all values of parameters of the problem. In peculiar cases, the characteristic function is expressed by elementary functions. Graphs of the probability density function are presented for a few cases. The article is a continuation of the author's previous paper. 相似文献
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Vibration characteristics of rectangular plates continuous over full range line supports or partial line supports have been studied by using a discrete method. Concentrated loads with Heaviside unit functions and Dirac delta functions are used to simulate the line supports. The fundamental differential equations are established for the bending problem of the continuous plate. By transforming these differential equations into integral equations and using the trapezoidal rule of the approximate numerical integration, the solution of these equations is obtained. Green function which is the solution of deflection of the bending problem of plate is used to obtain the characteristic equation of the free vibration. The effects of the line support, the variable thickness and aspect ratio on the frequencies and mode shapes are considered. By comparing the numerical results obtained by the present method with those previously published, the efficiency and accuracy of the present method are investigated. 相似文献
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《Physics letters. A》2006,355(1):32-38
Based on computerized symbolic computation, a complex hyperbolic-function method is proposed for the general nonlinear equations of mathematical physics in a unified way. In this method, we assume that exact solutions for a given general nonlinear equations be the superposition of different powers of the sech-function, tanh-function and/or their combinations. After finishing some direct calculations, we can finally obtain the exact solutions expressed by the complex hyperbolic function. The characteristic feature of this method is that we can derive exact solutions to the general nonlinear equations directly without transformation. Some illustrative equations, such as the ()-dimensional coupled Schrödinger–KdV equation, ()-dimensional Davey–Stewartson equation and Hirota–Maccari equation, are investigated by this means and new exact solutions are found. 相似文献
6.
Y. HattaT. Kunihiro 《Annals of Physics》2002,298(1):24-57
The so-called renormalization group (RG) method is applied to derive kinetic and transport equations from the respective microscopic equations. The derived equations include the Boltzmann equation in classical mechanics, the Fokker-Planck equation, and a rate equation in a quantum field theoretical model. Utilizing the formulation of the RG method which elucidates the important role played by the choice of the initial conditions, the general structure and the underlying assumptions in the derivation of kinetic equations in the RG method are clarified. It is shown that the present formulation naturally leads to the choice for the initial value of the microscopic distribution function at arbitrary time t0 to be on the averaged distribution function to be determined. The averaged distribution function may be thought of as an integral constant of the solution of the microscopic evolution equation; the RG equation gives the slow dynamics of the would-be initial constant, which is actually the kinetic equation governing the averaged distribution function. It is further shown that the averaging as given above gives rise to a coarse-graining of the time-derivative which is expressed with the initial time t0, and thereby leads to time-irreversible equations even from a time-reversible equation. It is shown that a further reduction of the Boltzmann equation to fluid dynamical equations and the adiabatic elimination of fast variables in the Fokker-Planck equation are also performed in a unified way in the present method. 相似文献
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基于人工可压缩性对密度的修正,本文用强隐式格式快速求解了非正交曲线坐标系下跨声速流函数方程;在流函数场解出后,通过求解一个由动量方程、能量方程和连续方程组合而成的关于密度的一阶偏微分方程来获得密度场,因此流函数解法中常遇到的密度双值问题在这里已不存在;通常所讲的完成流函数场{Ψ}与密度场{ρ}间的迭代在本文便体现在流函数主方程与这个新推出的一阶微分方程间的迭代计算上;几个典型算例表明了本方法的有效性。 相似文献
8.
Symmetries and conserved quantities of discrete wave equation associated with the Ablowitz-Ladik-Lattice system
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In this paper, we present a new method to obtain the Lie symmetries and conserved quantities of the discrete wave equation with the Ablowitz-Ladik-Lattice equations. Firstly, the wave equation is transformed into a simple difference equation with the Ablowitz-Ladik-Lattice method. Secondly, according to the invariance of the discrete wave equation and the Ablowitz-Ladik-Lattice equations under infinitesimal transformation of dependent and independent variables, we derive the discrete determining equation and the discrete restricted equations. Thirdly, a series of the discrete analogs of conserved quantities, the discrete analogs of Lie groups, and the characteristic equations are obtained for the wave equation. Finally, we study a model of a biological macromolecule chain of mechanical behaviors, the Lie symmetry theory of discrete wave equation with the Ablowitz-Ladik-Lattice method is verified. 相似文献
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A method to solve the Boltzmann equation is analyzed in the case when the distribution function depends on slow and fast time
and coordinate scales. Basic relationships for calculating the nonequilibrium multiscale distribution function are shown to
differ substantially from those found in the framework of the Chapman-Enskog method: the transfer equations are complemented
by the contributions of relaxation processes. The heat and momentum transfer equations derived from the general solution to
the Boltzmann equation involve additional terms accounting for relaxation effects. The relaxation effects included in the
energy equation result in both a hyperbolic heat conduction equation and a finite rate of heat transfer. In the viscous stress
tensor, the Newtonian term of the transfer equation turns out to be supplemented by relaxation terms. 相似文献
12.
用场方法来求解Whittaker方程.将一个场变量取作为其余场变量和时间的函数并对这个函数建立基本偏微方程.如能求得它的完全积分,那么Whittaker方程的解可由解代数方程来得到.
关键词:
场变量
基本偏微分方程
场方法
积分 相似文献
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Approximate direct reduction method: infinite series reductions to the perturbed mKdV equation
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The approximate direct reduction method is applied to the perturbed mKdV
equation with weak fourth order dispersion and weak dissipation. The
similarity reduction solutions of different orders conform to formal
coherence, accounting for infinite series reduction solutions to the
original equation and general formulas of similarity reduction
equations. Painlevé II type equations, hyperbolic secant and
Jacobi elliptic function solutions are obtained for zero-order
similarity reduction equations. Higher order similarity reduction
equations are linear variable coefficient ordinary differential
equations. 相似文献
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《Chinese Journal of Physics (Taipei)》2018,56(6):2916-2925
In this paper, an efficient numerical method is considered for solving space-time fractional wave equation. The fractional derivatives are described in the conformable sense. The method is based on shifted Chebyshev polynomials of the second kind. Unknown function is written as Chebyshev series with the N term. The space-time fractional wave equation is reduced to a system of ordinary differential equations by using the properties of Chebyshev polynomials. The finite difference method is applied to solve this system of equations. Numerical results are provided to verify the accuracy and efficiency of the proposed approach. 相似文献
17.
Similarity Reductions and Similarity Solutions of the (3+1)-Dimensional Kadomtsev-Petviashvili Equation 总被引:2,自引:0,他引:2
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Employing the compatibility method, we obtain the symmetries of the (3+1)-dimensional Kadomtsev Petviashvili (KP) equation. Four types of similarity reductions of the KP equation are obtained by solving the corresponding characteristic equations associated with symmetry equations. In addition, a lot of similarity solutions to the KP equation are obtadned. 相似文献
18.
Kinetic equations for the hard-sphere system are derived by diagrammatic techniques. A linear equation is obtained for the one-particle-one particle equilibrium time correlation function and a nonlinear equation for the one-particle distribution function in nonequilibrium. Both equations are nonlocal, noninstantaneous, and extremely complicated. They are valid for general density, since statistical correlations are taken into account systematically. This method derives several known and new results from a unified point of view. Simple approximations lead to the Boltzmann equation for low densities and to a modified form of the Enskog equation for higher densities. 相似文献
19.
Lutz E 《Physical review letters》2001,86(11):2208-2211
The influence functional method of Feynman and Vernon is used to obtain a quantum master equation for a system subjected to a Lévy stable random force. The corresponding classical transport equations for the Wigner function are then derived, both in the limits of weak and strong friction. These are fractional extensions of the Klein-Kramers and the Smoluchowski equations. It is shown that the fractional character acquired by the position in the Smoluchowski equation follows from the fractional character of the momentum in the Klein-Kramers equation. Connections among fractional transport equations recently proposed are clarified. 相似文献
20.
利用小扰动方法对非线性演化方程作展开得到原始方程的各级近似方程.应用Jacobi椭圆函 数展开法求得了零级近似方程的准确解,并由此得到一级近似方程和二级近似方程分别满足 齐次Lam方程和非齐次Lam方程,应用Lam函数和Jacobi椭圆函数展开法可以分别求得一级近似方程和二级近似方程的准确解.这样,就求得了非线性演化方程的多级准确解.
关键词:
Jacobi椭圆函数
Lam函数
多级准确解
非线性演化方程
扰动方法 相似文献